Study of lump solutions to dimensionally reduced generalized KP equations

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• 作者：Jian-Ping Yu ; Yong-Li Sun
• 关键词：Lump solutions ; Hirota bilinear equation ; Generalized bilinear equation ; (\(3+1\) ; ) ; Dimensional gKP equation
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：87
• 期：4
• 页码：2755-2763
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

In this paper, a new (\(3+1\))-dimensional generalized KP (gKP) equation is presented, and two classes of lump solutions, rationally localized in all directions in the space, to the dimensionally reduced cases in (\(2\,+\,1\))-dimensions are derived as well. The proposed method in this work is based on a Hirota bilinear differential equation, which implies that we can build the lump solutions to the presented reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Moreover, there are totally six free parameters in the resulting lump solutions, so that we can get the sufficient and necessary conditions guaranteeing analyticity and rational localization of the solutions by using these six free parameters. In the meantime, two special cases are plotted as illustrative examples and some contour plots with different determinant values are given to show that the corresponding lump solution tends to zero when the determinant approaches zero.